# 2 questions about dot product

1. Feb 13, 2013

### ericm1234

1. In the navier stokes equation we have the term ($\vec{u}$ $\bullet$∇)$\vec{u}$

If I have $\vec{u}$ = f(r)(-y,x) with r= $\sqrt{x^2+y^2}$ then is there some some of product rule/identity that needs to be invoked for the initial dot product?
I would say this calculation is:
(-y*f(r)$\frac{\partial}{\partial x}$ + x*f(r)$\frac{\partial}{\partial y}$) (-y*f(r),x*f(r))
Then:
(-y*f(r)*(0-y*$\frac{\partial f}{\partial r}$*$\frac{\partial r}{\partial x}$) + x*f(r)*(-f(r)-y*$\frac{\partial f}{\partial r}$*$\frac{\partial r}{\partial y}$), 2nd component)